Non-Commutative Mechanics in Mathematical & in Condensed Matter Physics

@article{Horvathy2006NonCommutativeMI,
  title={Non-Commutative Mechanics in Mathematical \& in Condensed Matter Physics},
  author={P. A. Horvathy},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2006},
  volume={2},
  pages={090}
}
  • P. Horvathy
  • Published 22 September 2006
  • Physics
  • Symmetry Integrability and Geometry-methods and Applications
Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1). Souriau’s construction applied to the two-parameter central extension of the planar Galilei group leads to the “exotic” particle, which has non-commuting position coordinates. A Berryphase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non… 
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